How does the network know which objects to track in the paper "Label-Free Supervision of Neural Networks with Physics and Domain Knowledge"?
They are not tracking anything, instead they are trying to find an object which satisfies free fall equation. Gravity acts the same regardless of object's properties - at least in vacuum. 

"In this paper, we model prior knowledge on the structure
of the outputs by providing a weighted constraint function
g used to penalize “structures” that are not
consistent with our prior knowledge."

There is a restriction to the possible parabola that is given in the last equation on page 2. They are training the Network to learn time dependence of that equation, which is the same for all objects.